技术领域：Technical field:
本发明涉及多元统计过程监测方法领域，更具体的说是涉及一种 基于裕度统计量的广义非负矩阵分解故障监测方法。The invention relates to the field of multivariate statistical process monitoring methods, in particular to a generalized non-negative matrix decomposition fault monitoring method based on margin statistics.
背景技术：Background technique:
面对现代工业过程日趋复杂的现状，只有实现了安全、稳定的运 行，才能获得最大的经济效益，因此，及时检测过程是否发生故障并 合理处理，具有重要的理论意义和工程应用价值。鉴于工业过程数据 反映了系统的内在变化和运转条件以及多元统计分析方法强大的特 征提取能力，为了保证制造安全以及生产质量，多元统计过程监控(Multivariate Statistical Process Monitoring,MSPM)引起了学术界和 工业界研究人员的高度重视，形成了一系列基于数据驱动的多元统计 过程监测方法。目前，广泛使用的多元统计方法主要有主成分分析 (Principal Component Analysis,PCA)、独立成分分析(Independent Component Analysis,ICA)和偏最小二乘法(Partial Least Squares,PLS)等。Faced with the increasingly complex status of modern industrial processes, the maximum economic benefits can only be obtained if safe and stable operation is achieved. Therefore, it is of great theoretical significance and engineering application value to detect whether a process fails in time and deal with it reasonably. In view of the fact that industrial process data reflect the internal changes and operating conditions of the system and the powerful feature extraction capabilities of multivariate statistical analysis methods, in order to ensure manufacturing safety and production quality, multivariate statistical process monitoring (Multivariate Statistical Process Monitoring, MSPM) has attracted academia and industry. With the high attention of researchers in the world, a series of data-driven multivariate statistical process monitoring methods have been formed. At present, the widely used multivariate statistical methods mainly include principal component analysis (Principal Component Analysis, PCA), independent component analysis (Independent Component Analysis, ICA) and partial least squares (Partial Least Squares, PLS).
非负矩阵分解(Non-negative Matrix Factorization,NMF)作为一 种新兴的多元统计技术，仅仅对原始数据有非负约束，并没有像潜变 量服从正态分布等的其他假设，并且在描述大规模高维数据的结构信 息，提取局部特征方面表现得优于PCA和ICA等传统方法。因此， 有理由相信，在故障检测与诊断技术的研究领域，NMF的思想也具 有很高的学术价值和广阔的应用前景，值得我们从学术和应用的角度 加以关注。Non-negative matrix factorization (Non-negative Matrix Factorization, NMF), as an emerging multivariate statistical technique, only has non-negative constraints on the original data, and has no other assumptions such as latent variables obeying a normal distribution, and is describing large-scale The structural information of high-dimensional data is better than traditional methods such as PCA and ICA in terms of extracting local features. Therefore, it is reasonable to believe that in the research field of fault detection and diagnosis technology, the idea of NMF also has high academic value and broad application prospects, and deserves our attention from the perspective of academic and application.
为此，有相关人员针对工业过程故障监测这个背景，对非负矩阵 分解方法展开了一系列的研究。Li等提出了利用NMF算法对非高斯 过程进行故障监测，并通过仿真实验验证了NMF算法应用于化工过 程故障监测的可行性，而且比传统的多元统计故障监测方法有更加广 泛的应用能力。王帆等提出了稀疏性非负矩阵分解(Sparse NMF, SNMF)算法，通过在NMF算法的基础上引入稀疏编码(Sparse Coding)方法得到对数据集更加稀疏的表示，通过TE过程的仿真验 证说明该方法相比于基本NMF算法具有明显的优越性。随后，Li等 针对工业过程负数数据存在的现象，提出了广义非负矩阵分解 (Generalized Non-negativeMatrix Factorization,GNMF)，主要目的是 减轻对原始数据的非负约束，虽然在监测效果上相比于其他传统的多 元统计方法有了一定的提高。For this reason, a series of studies have been carried out on the non-negative matrix factorization method against the background of industrial process fault monitoring. Li et al. proposed the use of NMF algorithm for fault monitoring of non-Gaussian processes, and verified the feasibility of applying NMF algorithm to chemical process fault monitoring through simulation experiments, and has wider application capabilities than traditional multivariate statistical fault monitoring methods. Wang Fan et al. proposed a sparse non-negative matrix factorization (Sparse NMF, SNMF) algorithm. By introducing a sparse coding (Sparse Coding) method on the basis of the NMF algorithm, a more sparse representation of the data set is obtained. The simulation verification of the TE process shows that Compared with the basic NMF algorithm, this method has obvious advantages. Subsequently, Li et al. proposed Generalized Non-negative Matrix Factorization (GNMF) in response to the phenomenon of negative data in industrial processes. The main purpose is to alleviate the non-negative constraints on the original data. Other traditional multivariate statistical methods have been improved to some extent.
传统的多元统计的故障监测方法，将原始数据变换后的潜变量的 加权数值与给定控制限的大小关系作为故障监测的依据，达到了一定 检测效果。但是该类方法忽视了不同采样时刻潜变量的相关性关系、 特征分布等，而且还需假设潜变量的性质满足特定分布，在监测精度 和灵敏度上还有待改进。The traditional multivariate statistical fault monitoring method uses the relationship between the weighted value of the latent variable after the transformation of the original data and the given control limit as the basis for fault monitoring, and achieves a certain detection effect. However, this type of method ignores the correlation relationship and characteristic distribution of latent variables at different sampling times, and also needs to assume that the properties of latent variables satisfy a specific distribution, and the monitoring accuracy and sensitivity need to be improved.
发明内容：Invention content:
本发明的目的是针对解决传统多元统计方法下的统计量利用潜 变量信息能力较差等问题，在传统的多元统计方法的基础上对不同采 样时刻的时变信息进行了分析，结合广义非负矩阵分解方法对数据分 布没有假设等特点，提出了一种基于裕度统计量的GNMF故障监测 方法(GNMF-Margin Statistics,GNMF-MS)。首先利用GNMF方法提 取过程的潜变量并求得传统意义下的统计量和控制上限。其次，在传 统统计量的基础上对过程数据构建二级控制限，并设定一定的控制裕 度。通过对不同采样时刻的时变信息进行了分析，对正常数据建立裕 度模型，计算二级控制限上重构的统计量，在原始的控制上限下进行 故障监测。最后通过对TE过程的仿真实验验证了该算法的可行性和 有效性。The purpose of the present invention is to solve the problem of poor ability to use latent variable information for statistics under the traditional multivariate statistical method. On the basis of the traditional multivariate statistical method, the time-varying information at different sampling moments is analyzed. The matrix decomposition method has no assumptions about the data distribution, etc., and a GNMF fault monitoring method based on margin statistics (GNMF-Margin Statistics, GNMF-MS) is proposed. Firstly, the GNMF method is used to extract the latent variables of the process and obtain the statistics and control upper limit in the traditional sense. Second, build secondary control limits for process data on the basis of traditional statistics, and set a certain control margin. By analyzing the time-varying information at different sampling times, a margin model is established for the normal data, the reconstructed statistics on the secondary control limit are calculated, and the fault monitoring is carried out under the original control upper limit. Finally, the feasibility and effectiveness of the algorithm are verified by the simulation experiment of TE process.
本发明的技术解决措施如下：Technical solutions of the present invention are as follows:
一种基于裕度统计量的广义非负矩阵分解故障监测方法，主要包 括离线建模和在线监测两个阶段，该方法包括如下步骤：A generalized non-negative matrix decomposition fault monitoring method based on margin statistics mainly includes two stages of off-line modeling and on-line monitoring. The method includes the following steps:
A、离线建模A. Offline modeling
1)数据预处理：对过程正常数据X(m×n)进行标准化处理；1) Data preprocessing: standardize the process normal data X(m×n);
2)初始化：使用SVD算法对广义非负矩阵分解(GNMF)进行 初始化，并利用式(1)迭代计算出基矩阵W；2) Initialization: use the SVD algorithm to initialize the generalized non-negative matrix factorization (GNMF), and use formula (1) to iteratively calculate the base matrix W;
其中，[Xij]+＝(|Xij|+Xij)/2，[Xij]-＝(Xij|-Xij)/2；Among them, [Xij ]+ = (|Xij |+Xij )/2, [Xij ]- = (Xij |-Xij )/2;
3)根据式(3)(4)求得传统正常数据的N2和SPE统计量，并通过 核密度估计(KDE)确定上述统计量的控制上限和SPEh；3) Obtain theN2 and SPE statistics of traditional normal data according to formula (3) (4), and determine the control upper limit of the above statistics by Kernel Density Estimation (KDE) and SPEh ;
当GNMF用于过程监测时，模型如式(2)所示When GNMF is used for process monitoring, the model is shown in formula (2)
其中，为特征空间，描述了过程中的状态变化，E则 表示为残差，描述了随机噪声；为了对故障进行监测，接下来构建两 个监测统计量指标，分别如式(3)、式(4)所示in, is the feature space, which describes the state changes in the process, E is represented as a residual, which describes random noise; in order to monitor the fault, two monitoring statistics indicators are constructed next, as shown in formula (3) and formula (4) respectively
其中，为原始数据X的重构；N2和SPE两个统计量都是 单变量，因此非常适合用核密度估计(KDE)这个方法来计算控制上 限；核密度估计是一类数据驱动的技术，用于密度函数的非参数估计；in, It is the reconstruction of the original data X; both N2 and SPE statistics are univariate, so it is very suitable to use the method of Kernel Density Estimation (KDE) to calculate the upper limit of control; Kernel Density Estimation is a kind of data-driven technology, using Based on the non-parametric estimation of the density function;
样本集X＝{xi,i＝1,2,…}，密度函数为P(x)，可以用式(5)表示The sample set X={xi ,i=1,2,…}, the density function is P(x), which can be expressed by formula (5)
而对单变量核估计的KDE方程如式(6)所示The KDE equation for univariate kernel estimation is shown in equation (6)
其中，是概率密度函数的估计，n是样本数，h是带宽，K(·) 是核函数，这里我们采用高斯核函数，且通常满足式(7)：in, is the estimate of the probability density function, n is the number of samples, h is the bandwidth, K( ) is the kernel function, here we use the Gaussian kernel function, and usually satisfy the formula (7):
这里我们采用该算法计算N2和SPE两个统计量指标的控制上限和SPEh，置信区间设为99％；Here we use this algorithm to calculate the control upper limit of the two statistical indicators of N2 and SPE and SPEh , with a confidence interval set at 99%;
B、在线监测B. Online monitoring
1)对新的过程数据进行相同的标准化处理；1) Perform the same standardization on new process data;
2)根据离线建模计算出的基矩阵W得到新的系数矩阵H；2) Obtain a new coefficient matrix H according to the base matrix W calculated by off-line modeling;
非负矩阵分解算法(NMF)：对于给定一个非负数据矩阵X∈Rm×n (m为数据变量数，n为数据样本数)，为找到一个近似的分解，将X 分解为一组适当的非负矩阵W∈Rm×k和H∈Rk×n使下式(8)成立：Non-negative matrix factorization algorithm (NMF): Given a non-negative data matrix X∈Rm×n (m is the number of data variables, n is the number of data samples), in order to find an approximate decomposition, decompose X into a set of Appropriate non-negative matrices W∈Rm×k and H∈Rk×n make the following formula (8) hold:
X+≈W+H+ (8)X+ ≈W+ H+ (8)
其中，W为基矩阵，H为系数矩阵，下角标”+”表示非负性约束， 降维阶次k一般情况下满足(m+n)k≤nm。而这种非负性约束导致了相 应的基矩阵W和系数矩阵H在一定程度上的稀疏性。Among them, W is the base matrix, H is the coefficient matrix, the subscript "+" indicates the non-negativity constraint, and the dimensionality reduction order k generally satisfies (m+n)k≤nm. And this non-negativity constraint leads to the sparsity of the corresponding base matrix W and coefficient matrix H to a certain extent.
NMF算法的分解问题可以归结为一个非线性优化问题，通过定 义一个目标函数来刻画低秩近似的逼近程度。Lee等定义了两种简单 的目标函数来解决该优化问题，并给出了W和H的迭代规则。本文 采用欧氏距离来度量原始数据矩阵X与基矩阵W和系数矩阵H之积之间的误差，其目标函数如式(9)所示：The decomposition problem of NMF algorithm can be attributed to a nonlinear optimization problem, by defining an objective function to describe the approximation degree of low-rank approximation. Lee et al. defined two simple objective functions to solve the optimization problem, and gave the iteration rules of W and H. In this paper, the Euclidean distance is used to measure the error between the original data matrix X and the product of the base matrix W and the coefficient matrix H, and its objective function is shown in formula (9):
对于上式，当X＝WH时取最小值0；而当上式的值越小越接近于 0的话，则说明分解越精确。这里我们采用乘法更新(MU)算法对 W和H进行迭代，更新规则如式(10)和式(11)所示：For the above formula, the minimum value is 0 when X=WH; and when the value of the above formula is smaller and closer to 0, it means that the decomposition is more accurate. Here we use the multiplicative update (MU) algorithm to iterate W and H, and the update rules are shown in formula (10) and formula (11):
式(9)中所示的目标函数是单调非增的，因此通过上述更新迭 代规则使得W和H不再变化时，则其目标函数保持不变。其中，基 矩阵W保留了原始数据的数据结构和空间关系，系数矩阵H则可作 为原始矩阵X的低阶近似矩阵。The objective function shown in formula (9) is monotonically non-increasing, so when W and H no longer change through the above update iteration rules, the objective function remains unchanged. Among them, the base matrix W retains the data structure and spatial relationship of the original data, and the coefficient matrix H can be used as a low-order approximate matrix of the original matrix X.
3)计算监测统计量和SPEMS；3) Calculation of monitoring statistics and SPEMS ;
(a)离线裕度和二级控制限的设定(a) Setting of off-line margin and secondary control limit
由正常数据的统计量数值分布可知，其数值分布与给定控制限之 间存在相应裕度，这部分裕度信息有利于微小故障数据的分离，因此， 在原有控制限的前提下，基于裕度信息定义二级的控制限和SPEl， 该控制限不仅指示了正常数据的统计量数值分布水平，又保证了与给 定控制上限和SPEh之间的允许波动范围，更有利于故障监测；It can be seen from the numerical distribution of normal data statistics that there is a corresponding margin between the numerical distribution and the given control limit. This part of the margin information is conducive to the separation of small fault data. Therefore, under the premise of the original control limit, based on the margin degree information defines the control limits for the second level and SPEl , the control limit not only indicates the distribution level of the statistic value of the normal data, but also guarantees the same as the given control upper limit The allowable fluctuation range between and SPEh is more conducive to fault monitoring;
这里我们假设对SPE(t)统计量进行改善，首先在原有的正常数据 的监测统计量控制上限SPEh的基础上求出一个控制上限SPEh和统计量 SPE(t)均值的差关于SPE(t)方差的倍数f如式(13)所示：Here we assume that the SPE(t) statistic is improved. First, on the basis of the original normal data monitoring statistic control upper limit SPEh , the difference between the upper control limit SPEh and the mean value of the statistic SPE(t) is calculated. About SPE( The multiple f of the variance of t) is shown in formula (13):
f＝(SPEh-SPE_mean)/SPE_std (12) 其中，SPE_mean和SPE_std分别为SPE的均值的方差。f=(SPEh −SPE_mean)/SPE_std (12) where, SPE_mean and SPE_std are respectively the variance of the mean value of SPE.
由于正常数据到故障数据往往会存在着一定的容许裕度，为此我 们根据正常数据的允许范围，降低了一倍方差设定了一个二级控制限 SPEl。并根据SPEl求得其与各采样时刻SPE统计量与二级控制限SPEl的 裕度Dist。Dist保证了时变过程中正常情况的特征范围。SPEl可由式 (13)所得：Since there is often a certain allowable margin between normal data and fault data, we set a secondary control limit SPEl according to the allowable range of normal data and doubled the variance. And according to SPEl , the margin Dist between it and the SPE statistics at each sampling time and the secondary control limit SPEl is obtained. Dist guarantees a characteristic range for normal cases in time-varying processes. SPE1 can be gained by formula (13):
SPEl＝SPE_mean+(f-1)·SPE_std (13)SPEl = SPE_mean + (f-1) SPE_std (13)
这里我们引入对过程数据的时变分析，接下来计算第i个采样时 刻统计量SPE(t)的一阶、二阶差分如式(14)：Here we introduce the time-varying analysis of process data, and then calculate the first-order and second-order differences of the i-th sampling time statistic SPE(t) as shown in formula (14):
因此，二级控制限SPEl的统计量裕度dist可由式(15)拟合：Therefore, the statistical margin dist of the secondary control limit SPEl can be fitted by formula (15):
dist(t)＝a×E1(t)+b×E2(t)+c×SPE(t) (15)dist(t)=a×E1 (t)+b×E2 (t)+c×SPE(t) (15)
其中，a,b,c为对应系数。并通过下式的优化目标进行最优参数求解对 应的系数如式(16)：Among them, a, b, c are corresponding coefficients. And through the optimization objective of the following formula to solve the optimal parameters, the corresponding coefficients are as formula (16):
||a||,||b||,||c||≤1||a||,||b||,||c||≤1
(b)在线统计量的构造(b) Construction of online statistics
在线监测中，同样地计算故障数据下第i个采样时刻的统计量 SPEf(t)的一阶、二阶差分Ef1和Ef2，如式(17)：In online monitoring, the first-order and second-order differences Ef1 and Ef2 of the statistic SPEf (t) at the i-th sampling time under the fault data are also calculated, as shown in formula (17):
故障数据下的重构统计量裕度可由式(18)构造：The reconstruction statistics margin under fault data can be constructed by formula (18):
distf(t)＝a×Ef1(t)+b×Ef2(t)+c×SPEf(t) (18)distf (t) = a×Ef1 (t)+b×Ef2 (t)+c×SPEf (t) (18)
其中，a,b,c三个对应系数由式(16)求得。Among them, the three corresponding coefficients of a, b, and c are obtained from formula (16).
而在故障监测中新的裕度统计量SPEMS由式(19)计算得到：In fault monitoring, the new margin statistic SPEMS is calculated by formula (19):
4)通过比较监测统计量和SPEMS和相应控制上限和SPEh，判 断其是否为故障；当新的样本数据在线得到后，新的统计量SPEMS和 原始正常数据控制上限SPEh进行比较；当SPEMS>SPEh时，即表示过程 可能产生了故障，需要进行进一步的分析和验证。4) Monitor statistics by comparing and SPEMS and corresponding upper control limits and SPEh to determine whether it is a fault; when the new sample data is obtained online, the new statistic SPEMS is compared with the original normal data control upper limit SPEh ; when SPEMS > SPEh , it means that the process may have produced Faults require further analysis and verification.
本发明的有益效果在于：The beneficial effects of the present invention are:
本发明由于传统多元统计方法下的统计量存在着利用潜变量信 息能力较差等问题，为此，在其基础上设定了一定的控制裕度，并且 对不同采样时刻的时变信息进行了分析，结合广义非负矩阵对数据分 布没有假设等优点，提出了一种基于裕度统计量的广义非负矩阵分解 故障监测方法。TE仿真实验的结果表明，与PCA和ICA等传统故障 监测方法相比，本文所提方法在一定程度上是有成效的。In the present invention, due to the poor ability to use latent variable information in the statistics under the traditional multivariate statistical method, a certain control margin is set on the basis of the statistics, and the time-varying information at different sampling times is analyzed. Combining the advantages of generalized nonnegative matrix without assumptions about data distribution, a generalized nonnegative matrix factorization fault monitoring method based on margin statistics is proposed. The results of TE simulation experiments show that compared with traditional fault monitoring methods such as PCA and ICA, the method proposed in this paper is effective to a certain extent.
附图说明：Description of drawings:
下面结合附图对本发明做进一步的说明：Below in conjunction with accompanying drawing, the present invention will be further described:
图1为本发明的流程示意图；Fig. 1 is a schematic flow sheet of the present invention;
图2为TE过程工艺流程图；Figure 2 is a flow chart of the TE process;
图3为正常数据的统计量与其控制限的关系；Figure 3 is the relationship between the statistics of normal data and its control limits;
图4为GNMF在故障19上的监测效果；Figure 4 shows the monitoring effect of GNMF on fault 19;
图5为GNMF-MS在故障19上的监测效果。Figure 5 shows the monitoring effect of GNMF-MS on fault 19.
具体实施方式：Detailed ways:
结合附图1～5和具体实施例，对本发明作进一步详细说明，一种 基于裕度统计量的广义非负矩阵分解故障监测方法，主要包括离线建 模和在线监测两个阶段，包括如下步骤：In conjunction with accompanying drawings 1 to 5 and specific embodiments, the present invention will be further described in detail. A generalized non-negative matrix decomposition fault monitoring method based on margin statistics mainly includes two stages of offline modeling and online monitoring, including the following steps :
A、离线建模：1)数据预处理。对过程正常数据X(m×n)进行标准 化处理；2)初始化：使用SVD算法对GNMF进行初始化，并利用迭 代计算出基矩阵W；3)求得传统正常数据的N2和SPE统计量，并通过 KDE确定上述统计量的控制上限和SPEh。A. Offline modeling: 1) Data preprocessing. Standardize the process normal data X(m×n); 2) Initialize: use the SVD algorithm to initialize the GNMF, and use iteration to calculate the base matrix W; 3) Obtain the N2 and SPE statistics of the traditional normal data, And determine the upper control limit of the above statistics by KDE and SPEh .
B、在线监测：1)对新的过程数据进行相同的标准化处理；2)根 据离线建模计算出的基矩阵W得到新的系数矩阵H；3)计算监测统计 量和SPEMS；4)通过比较监测统计量和SPEMS和相应控制上限和SPEh，判断其是否为故障。B. On-line monitoring: 1) Perform the same standardization process on the new process data; 2) Obtain a new coefficient matrix H based on the base matrix W calculated by off-line modeling; 3) Calculate monitoring statistics and SPEMS ; 4) monitor statistics by comparison and SPEMS and corresponding upper control limits and SPEh to determine whether it is a fault.
TE(Tennessee-Eastman)过程由美国田纳西-伊斯曼化学品公司 所创建，是一个被国际上所公认适用于评价监控方法的真实工业过程 仿真平台，作为比较各种方法的数据源，被大量学者广泛地应用于故 障检测与诊断的研究，其工艺流程图如图2所示。The TE (Tennessee-Eastman) process was created by the Tennessee-Eastman Chemical Company in the United States. It is an internationally recognized real industrial process simulation platform suitable for evaluating monitoring methods. As a data source for comparing various methods, it has been widely used Scholars are widely used in the research of fault detection and diagnosis, and its process flow chart is shown in Figure 2.
TE过程包括5个主要单元：反应器、冷凝器、压缩机、分离器 和气提塔；包括A～H总共种成分，其中A、C、D、E为反应物，B 为催化剂，G、H为最终的产物；共41个测量变量和12个控制变量， 共52个观测变量；正常工况的960个样本数据采自过程平稳的运行 状态，各个故障工况数据前160个时刻的样本为正常数据，后800个 时刻的样本为故障数据。过程共设置了21种故障状况，其中故障 16～20未知，详细描述见表1。The TE process includes 5 main units: reactor, condenser, compressor, separator and stripping tower; including A~H total components, where A, C, D, E are reactants, B is catalyst, G, H is the final product; a total of 41 measured variables and 12 control variables, a total of 52 observed variables; 960 sample data of normal working conditions are collected from the smooth running state of the process, and the samples of the first 160 moments of each fault working condition data are Normal data, and the samples at the last 800 moments are fault data. A total of 21 fault conditions were set in the process, of which faults 16 to 20 are unknown, and the detailed description is shown in Table 1.
表1 TE过程故障描述Table 1 TE process fault description
仿真实验Simulation
本实施例选取33个变量(22个测量变量和11个控制变量)的 过程数据进行分析。在PCA方法中，通过SVD得到的PCs为14， 相应的，GNMF中的NCs个数也为14。为了验证所提新的监测统计 量方法的可行性，首先离线观测正常数据的传统统计量及其相应传统 控制上限和二级控制限的关系，如图3所示，其中虚线为控制上限， 实线为二级控制限。In this embodiment, the process data of 33 variables (22 measured variables and 11 controlled variables) are selected for analysis. In the PCA method, the number of PCs obtained by SVD is 14, and correspondingly, the number of NCs in GNMF is also 14. In order to verify the feasibility of the proposed new monitoring statistics method, firstly observe the traditional statistics of normal data offline and the relationship between the corresponding traditional control upper limit and the secondary control limit, as shown in Figure 3, where the dotted line is the control upper limit, and the actual The line is the secondary control limit.
从图3中可以看出正常数据的数值分布与其控制上限存在着一 定的裕度，该部分裕度信息不仅有利于提升故障监测的效果，更为所 提新的统计量提供了先验条件，保证了数据在控制上限与二级控制限 之间的允许波动范围。以TE过程的故障19为例，将GNMF-MS方 法与GNMF方法进行比较，监测效果如图4和图5所示。It can be seen from Figure 3 that there is a certain margin between the numerical distribution of normal data and its control upper limit. This part of the margin information is not only conducive to improving the effect of fault monitoring, but also provides a priori conditions for the proposed new statistics. The allowable fluctuation range of the data between the upper control limit and the secondary control limit is guaranteed. Taking fault 19 in the TE process as an example, comparing the GNMF-MS method with the GNMF method, the monitoring results are shown in Figures 4 and 5.
从图4和图5中可以较明显的看出，虽然两种算法在N2和统 计量上的监测效果并不是很好，尤其是GNMF算法，无法对故障进 行监测，但相对于前者，本文所提算法的监测效果有所提高；对于在 SPE和SPEMS统计量监测效果的比较，GNMF算法的漏报率高达91.50％，GNMF-MS算法却能有效地监测故障，并使得漏报率降至 11.74％，总监测率也提高到了88.54％，监测提升的效果较明显。It can be clearly seen from Figure 4 and Figure 5 that although the two algorithms are in the range of N2 and The monitoring effect on the statistics is not very good, especially the GNMF algorithm, which cannot monitor the fault, but compared with the former, the monitoring effect of the algorithm proposed in this paper has been improved; for the comparison of the monitoring effect of the SPE and SPEMS statistics , the false negative rate of the GNMF algorithm is as high as 91.50%, but the GNMF-MS algorithm can effectively monitor the fault, and the false positive rate is reduced to 11.74%, and the total detection rate is also increased to 88.54%. The effect of monitoring improvement is more obvious.
为进一步验证本文算法的有效性，与PCA、ICA和GNMF方法 进行综合比较分析。对于4种方法都能较有效检测出的故障，这里我 不再进行分析讨论，故对余下的故障进行了实验分析比较。表2为4 种方法的监测结果，并对最高故障监测率加粗显示。In order to further verify the effectiveness of the algorithm in this paper, a comprehensive comparative analysis is carried out with PCA, ICA and GNMF methods. For the faults that can be detected more effectively by the four methods, I will not analyze and discuss them here, so the remaining faults are analyzed and compared experimentally. Table 2 shows the monitoring results of the four methods, and the highest fault monitoring rate is shown in bold.
表2 为PCA，ICA，GNMF和GNMF-MS 4种方法在TE过程的 故障监测率Table 2 shows the fault detection rate of the four methods of PCA, ICA, GNMF and GNMF-MS in the TE process
首先，可以从表中看出GNMF方法在监测效果上有所提升，相比 于PCA和ICA方法有着更高的监测率，凸显了GNMF方法对潜变量 没有假设的这个特点。然后可以从表1中进一步的看出4种方法在在 故障3、故障5、故障9、故障15、故障16和故障21的监测率都不 是很高。但是相对于其他三种方法，本文所提方法在一定程度上提高 了监测精度；对于故障10、故障11、故障19和故障20，GNMF-MS 方法的监测率相较于其他三种方法的最高监测率分别提高了 30.32％，19.79％，64.89％和16.78％；对于故障4，故障8和故障17， 本文所提方法与其他三种方法也相差不大。综合来说，本文所提的 GNMF-MS方法在监测效果上相比于其他三种方法，有了一定程度的 提高，尤其是在SPEMS统计量上的监测效果。First of all, it can be seen from the table that the GNMF method has improved the monitoring effect, and has a higher monitoring rate than the PCA and ICA methods, highlighting the fact that the GNMF method has no assumptions about latent variables. Then it can be further seen from Table 1 that the monitoring rates of the four methods in fault 3, fault 5, fault 9, fault 15, fault 16 and fault 21 are not very high. However, compared with the other three methods, the method proposed in this paper improves the monitoring accuracy to a certain extent; for fault 10, fault 11, fault 19 and fault 20, the monitoring rate of the GNMF-MS method is the highest compared with the other three methods. The monitoring rate increased by 30.32%, 19.79%, 64.89% and 16.78% respectively; for fault 4, fault 8 and fault 17, the method proposed in this paper is not much different from the other three methods. In general, the GNMF-MS method proposed in this paper has a certain degree of improvement in monitoring effect compared with the other three methods, especially in the monitoring effect of SPEMS statistics.
本发明由于传统多元统计方法下的统计量存在着利用潜变量信 息能力较差等问题，为此，在其基础上设定了一定的控制裕度，并且 对不同采样时刻的时变信息进行了分析，结合广义非负矩阵对数据分 布没有假设等优点，提出了一种基于GNMF的改进统计量故障监测 方法。TE仿真实验的结果表明，与PCA和ICA等传统故障监测方法 相比，本文所提方法在一定程度上是有成效的。In the present invention, due to the poor ability to use latent variable information in the statistics under the traditional multivariate statistical method, a certain control margin is set on the basis of the statistics, and the time-varying information at different sampling times is analyzed. Combining the advantages of generalized non-negative matrix without assumptions about data distribution, an improved statistical fault monitoring method based on GNMF is proposed. The results of TE simulation experiments show that compared with traditional fault monitoring methods such as PCA and ICA, the method proposed in this paper is effective to a certain extent.
上述实施例是对本发明进行的具体描述，只是对本发明进行进一 步说明，不能理解为对本发明保护范围的限定，本领域的技术人员根 据上述发明的内容作出一些非本质的改进和调整均落入本发明的保 护范围之内。The above-mentioned embodiment is a specific description of the present invention, only to further illustrate the present invention, and can not be understood as limiting the protection scope of the present invention. Those skilled in the art can make some non-essential improvements and adjustments according to the content of the above-mentioned invention, which all fall into the scope of this invention. within the scope of protection of the invention.
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| CN201710874382.4ACN107861492A (en) | 2017-09-25 | 2017-09-25 | A kind of broad sense Non-negative Matrix Factorization fault monitoring method based on nargin statistic |
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